Spell checking is easier than ever given that most browsers now have either spell check automatically built already or can easily be added. Even if a browser does not have spell check there are still several other ways users can spell check their text. So there really is no reason why people can not get a spell check done. It only takes a few seconds (and in cases of browsers, spell checking may be done automatically while typing to show you all words you have spelled incorrectly just like in Microsoft Office suite since 1997.)
Opera's newer versions (since version 10 on) come with your default language spell check loaded in on install. Changing your language spell check is extremely easy too.
Right click on an open text box, at the bottom of the menu look for “dictionaries”. Click “Add/remove dictionaries” then look for the language you want from their menu. Click the check box beside the one you want and then click “next”. The browser will automatically download the spell check library and install it with no restart required. You will have to agree to their terms of use though. (Their terms of use is basically that you can't sell their list as your own.)
Chrome also has built in spell checking. ( more on that here.)
Firefox has a spell checker though it may need to be enabled before you can use it… This page talks all about Firefox's spell check.
Given that the internet has a ton of uses, some people have taken it upon themselves to set up their own spell checking websites so users without spell check can get one done quickly and easily when they want/need one. So here is a list of some online spell checkers:
Spell check is not perfect. There are many times when spell check cannot help you. Cases where a word is spelled correctly, but it is the wrong word for the sentence. For example: “I eight lunch today, it was real goof.” In that sentence spell check would not trigger despite “eight” and “goof” being wrong for that sentence. What this means is that users cannot rely solely on spell check to catch every mistake. Spell check is good at spotting mistakes, but only if words are spelled wrong and not used incorrectly. So it is a good idea to always re-read your work before you press the post/submit button.